In the late 1960s and 1970s, a serial killer calling himself Zodiac terrorised northern California. Though he repeatedly corresponded with police, press and public, he was never caught.

Murder

Zodiac Photograph: Allstar/PARAMOUNT/Sportsphoto Ltd./Allstar

A young couple park their car in a quiet spot after dark. Meanwhile, someone else is watching – and waiting. It's a classic horror film set-up, except this really happened on 4 July 1969 in Vallejo, California. It was the second confirmed double shooting by the Zodiac killer (the female victim, Darlene Ferrin, was killed; her companion, Mike Magneau, survived). The gunman called police just after midnight to report his own crime, and also claimed to have killed "those kids last year". The switchboard operator noted he seemed to be speaking from a script. On 1 August, letters from the killer containing details about the murder and mysterious cryptograms were received by three newspapers in the area. It's all brilliantly recreated in the movie, with exquisite attention to detail.

People

One of the newspapers that receives a Zodiac letter is the San Francisco Chronicle, where reporter Paul Avery (Robert Downey Jr) takes up the case. But it's the paper's cartoonist, Robert Graysmith (Jake Gyllenhaal), who really develops a fixation on it. Movies need heroes, and it's probably inevitable – because Graysmith turned amateur sleuth and eventually wrote a bestselling book on the case – that he becomes one here. Some Zodiac case enthusiasts won't like this. Graysmith's analysis is not universally accepted. What makes Zodiac unusual as a historical movie is that it doesn't try to pretend its hero is perfect. In fact, it deliberately includes a few of Graysmith's wackier moments, like trying to match the killings to lunar cycles, badgering witnesses, and getting carried away with his own fame. On the other hand, it has cast Jake Gyllenhaal, who is a fine actor but just can't help looking like an adorable puppy at all times. So he adorably becomes obsessed with a serial killer, and adorably neglects his wife and children, and adorably names suspects based on his own unorthodox investigations. Aww! So cute. He can't be a baddie.

Crimes

Though Zodiac claimed 37 killings, there were five canonical Zodiac murder victims and two survivors. The movie also brings in the possible additional Zodiac cases of Cheri Jo Bates, murdered in 1966, and Kathleen Johns, abducted along with her baby daughter in 1970, who managed to escape. Many directors would have been tempted to play up the Johns case for maximum horror-movie effect, perhaps showing her running through the woods while Zodiac chased her with a flashlight. Whether that happened or not is disputed. Initial police reports seem to disagree with Johns's later testimony. Director David Fincher charts a historically judicious course, and doesn't show her escape at all. He may have made Se7en, but with Zodiac he proves he's no sensationalist.

Suspects

Despite (or because of) its restraint, Zodiac remains utterly compelling. Few screenplays successfully weave into one narrative such a large ensemble of characters, as well as a series of events scattered over 23 years. This one does, and with style. Like Graysmith's book, it settles on one named suspect as the probable Zodiac. This is open to question: there were 2,500 suspects (including the Unabomber, Theodore Kaczynski) and at least half a dozen credible names. Even if you take issue with its theory, though, the film wins historical points for openly admitting that it's not watertight. As it says, all the evidence in favour of its suspect's candidacy was circumstantial. A handwriting test disqualified him (as did a DNA test in 2002, though that date is outside the purview of the movie). There was one piece of direct evidence – but the movie finishes on it, so I'm not going to give it away.

Verdict

You may not agree with all of Zodiac's conclusions, but it makes its case credibly and allows space for disagreement. It's a perfect example of how a historical film can be accurate, balanced in opinion, and a gripping thriller – all at the same time.